Risk Management Systems based on Risk Factor Scenario Generation are widely used by financial institutions, resource-based corporations, trading organizations, governments, and other users (referred to herein as institutions) for the purposes of risk characteristics' estimation, risk analysis and management, and portfolio optimization. Risk factors can comprise a variety of data, including interest rates or rate spreads, foreign exchange rates, market indices, macroeconomic variables, etc. A risk factor scenario represents a hypothetical market situation and generally comprises values for the risk factors and an assigned probability of occurrence.
Risk Management Systems based on Risk Factor Scenario Generation are used in satisfying the everyday needs of the institutions to answer questions like “What will happen to the value (or other characteristic) of the institution's portfolio if Dow Jones goes 300 points down and the 2 year Treasury rates up to 10% tomorrow?” or “What is the maximum possible loss of the institution's portfolio over a period of 5 days at a predefined probability level?” —the so-called Value-at-Risk (VaR) measure. By answering these and similar questions, managers identify appropriate hedging strategies, establish the amount of the necessary economic capital, and actively manage the risk exposures of the institution.
Institutions commonly employ Risk Management Systems based on risk factor scenario generation for the purposes of risk analysis and portfolio management including but not limited to Value-at-Risk and Credit Value-at-Risk analysis, and portfolio optimization.
The Market Risk Management Systems employ scenario generation in order to obtain possible values for risk factors such as exchange rates, stock prices, interest rates, etc. at the time of the analysis horizon. Each of the instruments (positions) in the portfolio under consideration is then re-valuated according to each realized scenario for the risk factors affecting the price of the instrument (position). Afterwards the sample distribution function of the portfolio is obtained and the required risk characteristics such as Value-at-Risk, Shortfall etc. are calculated.
The proper generation of the possible values for the risk factors is the key factor for a realistic estimation of the final results.
In Credit Risk Systems the problem is quite alike, but usually the risk factors are of different nature—such as credit spreads, industry indices and macro-variables. In such systems the credit quality of counterparty is generally based on the realizations of the variables such as industry indices and macro-factors that affect the creditworthiness of the counterparty. Having scenarios for these variables, the value of the exposure to a given counterparty is obtained under each scenario. Then the sample distribution function for the portfolio comprising all the exposures is obtained and the required credit risk characteristics such as Credit Value-at-Risk, Credit Shortfall etc. are calculated. The proper determination of possible scenarios for the drivers (risk factors) of credit events is a key factor for the realistic determination of the risk characteristics.
Portfolio Optimization Systems go one step further and aim at identifying the portfolio structure that in general keeps the return on the same level as in the current portfolio (or on other pre-specified level) and simultaneously improves (minimizes) a chosen risk characteristic. The user may alternatively choose to maximize the return keeping the level of the risk characteristic, or specify any appropriate utility function. Most of the methods for portfolio optimization require a set of scenarios for a selected universe of instruments as an input argument. The latter are usually obtained by applying proper valuation models to the scenarios for the risk factors that affect the instruments' prices. In this respect, a Portfolio Optimization System can be viewed as an extended Risk Management System.
To summarize, Risk Management Systems generally perform the following steps: first—generation of scenarios for relevant risk factors, second—obtaining relevant characteristic for each instrument under consideration according to every risk factor scenario, third—calculating final results on the basis of the previously obtained instrument characteristics under the different risk factor scenarios. The final results within a Risk Management System, as mentioned above, comprise: Value-at-Risk and Shortfall of the portfolio representing the analyzed set of instruments for Market Risk Management System; Credit Value-at-Risk and Credit Shortfall for Credit Risk Management System; optimal allocation of the capital among the analyzed set of instruments for Portfolio Optimization System. The latter description is not aimed at narrowing the possible outputs and uses of a Risk Management System, but rather at offering the reader an intuition for the scope of the problem.
The first step of the process described above is Risk Factor Scenario Generation; the second is Instrument Characteristics Estimation; the third is Risk Characteristics Estimation.
Risk Management Systems generally use three approaches to obtain risk factor scenarios: first—user-defined scenarios, second—scenarios obtained from historical market data observations (the so-called empirical scenarios) and third—scenarios based on simulation of random variables with a pre-defined probabilistic distribution.
Due to the fast growing complexity of financial markets, the rapidly changing environment and the sudden market downturns, it becomes vitally important for institutions to employ Risk Management Systems capable of generating risk factor scenarios and estimating risk characteristics in an accurate and representative way.
The rapidly changing financial environment makes the use of empirical scenarios obsolete and unreliable. Moreover, such a method assumes that the only events that might occur in the future are those already observed in the past, the latter posing an unrealistic limitation.
Other commonly used Risk Factor Scenario Generation methods within Risk Management Systems are based on the assumption that risk factors' returns have multivariate normal distribution. The multivariate normal distribution then provides a straightforward method to produce scenarios. These methods are known to produce non-realistic results in attempt to model extreme events thus often underestimating the risk characteristics.
Despite this problem, currently there are no serious attempts to employ more sophisticated distributional functions for describing the behavior of risk factors. A major reason for the latter is that the computational time for evaluating parameters of a complex distribution function for a great number of risk factors well exceeds the reasonable time limit for performing a risk analysis.
Many independent academic researchers have proposed various interesting algorithms for more adequate modeling of the financial variables. However, none of these methods goes beyond the scope of purely academic research and/or the algorithms proposed are not suitable for the multi-dimensional nature of financial reality. See RiskMetrics “Return to RiskMetrics: The Evolution of a Standard” April 2001, p. 25: “However, it has often been argued that the true distribution of returns (even after standardizing by the volatility) implies a larger probability of extreme returns than that implied from the normal distribution. Although we could try to specify a distribution that fits returns better, it would be a daunting task, especially if we consider that the new distribution would have to provide a good fit across all asset classes. There has been a lot of discussion of these issues and some alternative distributions have been proposed. But up until now academics as well as practitioners have not agreed on an industry standard heavy-tailed distribution (or family of distributions).”
Another problem of proper generation of risk factor scenarios, as pointed above, is the complexity of financial markets. A typical bank portfolio relies on thousands of risk factors with various natures—interest rates, exchange rates, market indices, implied volatilities, credit spreads, etc. Each of them possesses different characteristics, different variability behavior and, moreover, the dependencies between sub-sets of the risk factors can be of diverse nature. Thus, the underlying probabilistic model from which financial risk factor scenarios are sampled must be very flexible.
There are numerous publications on copula approach in finance (see for example the works of Embrechts Paul). However, all of these research papers deal only with modeling the dependency of financial returns but not with the entire distribution. None of the papers discusses issues related to the practicability of the proposed models and does not report computational requirements and an execution time.
In the book of Rachev, S. T., Mittnik, K., Stable Paretian Models In Finance, John Wiley and Sons Ltd. 2001, it is proposed to model financial series by multivariate sub-Gaussian model. This model results in symmetric stable Paretian distributions for each financial series under consideration. However, a shortcoming of this model is that all marginal distributions must have the same index of stability, which implies that every risk factor has equally heavy tails. The latter means that the probability of an extreme event is equal for each risk factor after normalization. This is the first difference from the present invention. As a second point, the book provides only a mathematical model without proposing a method, framework, or system for its real application for solving practical problems.
In the Mercury 1.5 risk management software application developed by the applicant, the idea of using stable sub-Gaussian models to model financial returns is modified and implemented in computer algorithm. Mercury 1.5 is an important step ahead in the development of Risk Management Software, since it is the first attempt to model financial variables (risk factors) with more flexible and realistic distributions.
However, there are certain deficiencies:                The dependencies are considered to exist only in the center of the distributions of financial series, which means that extreme events happen independently across different securities. That contradicts to the financial reality.        The system suffers in many aspects from its monolithic architecture. Each step in the risk factor scenario generation process is executed every time the system is run. The latter creates speed performance problems and limits the user's flexibility.        It determines only a VaR figure and does not allow for thorough scenario analysis that is crucial for risk managers.        